5.6 Diastereomers

Stereoisomers

Stereoisomers share the same molecular formula and connectivity but differ in how their atoms are arranged in 3D space. The two main categories are enantiomers (mirror images) and diastereomers (non-mirror images). This distinction matters because it determines whether two molecules will have identical or different physical properties, which directly affects how they behave in reactions and biological systems.

Enantiomers vs Diastereomers

Enantiomers are non-superimposable mirror images of each other, like your left and right hands. They have opposite configurations at every chirality center (every R becomes S, and vice versa). Their physical properties (melting point, boiling point, solubility) are identical in achiral environments. The only difference you can measure directly is the direction they rotate plane-polarized light: one rotates it clockwise (+), the other counterclockwise (−).

Diastereomers are stereoisomers that are not mirror images. They differ in configuration at one or more chirality centers, but not at all of them. This is the key distinction: if you flip every center, you get the enantiomer; if you flip only some, you get a diastereomer.

Because diastereomers aren't mirror images, they have genuinely different physical properties:

• Different melting points and boiling points
• Different solubilities
• Different densities and refractive indices

This means you can separate diastereomers using ordinary techniques like recrystallization or chromatography, unlike enantiomers, which require chiral resolving agents.

Cis/trans isomers are a common example of diastereomers. Cis-2-butene and trans-2-butene have the same connectivity but aren't mirror images, and they have different boiling points.

Stereoisomer Quantity Calculation

The maximum number of possible stereoisomers for a molecule is given by:

$2^n$

where $n$ is the number of chirality centers (stereocenters).

• A molecule with 2 chirality centers: $2^2 = 4$ stereoisomers
• A molecule with 3 chirality centers: $2^3 = 8$ stereoisomers

These stereoisomers organize into pairs:

• Enantiomeric pairs: $2^{n-1}$ pairs (each stereoisomer has exactly one enantiomer)
• Diastereomeric relationships: every pair of stereoisomers that isn't enantiomeric is diastereomeric

For a molecule with 2 chirality centers, you get 2 enantiomeric pairs. Any molecule from one pair is a diastereomer of any molecule from the other pair, giving you 4 diastereomeric pairings total.

Meso compounds are the important exception. A meso compound has multiple chirality centers but is achiral overall because it contains an internal plane of symmetry. The molecule can be superimposed on its mirror image, so it doesn't have a distinct enantiomer.

Tartaric acid is the classic example. With 2 chirality centers, you'd predict $2^2 = 4$ stereoisomers. But one of the expected "pair" is actually a single meso compound (the (R,S) form equals the (S,R) form). So tartaric acid has only 3 stereoisomers: one (R,R), one (S,S), and one meso. Whenever a meso compound exists, the actual number of stereoisomers is less than $2^n$.

Epimers and Stereoisomer Relationships

Epimers are a specific subset of diastereomers that differ in configuration at exactly one chirality center. Think of them as the "closest" diastereomers in terms of structural similarity.

Glucose and galactose are epimers: they differ only at C-4. Every other chirality center has the same configuration. This makes them structurally very similar, which means:

• Their physical properties are closer to each other than those of diastereomers differing at multiple centers, making them harder to separate
• Despite their similarity, they have very different biochemical roles (your body metabolizes glucose and galactose through different pathways)

To keep the relationships straight:

• Enantiomers differ at all chirality centers
• Epimers differ at exactly one chirality center
• Other diastereomers differ at more than one but fewer than all chirality centers

Stereoisomer Representations

Fischer projections are a standard way to draw stereoisomers on paper, especially for molecules with multiple chirality centers (like sugars and amino acids). The convention is:

• Horizontal lines represent bonds pointing out of the page (toward you)
• Vertical lines represent bonds pointing into the page (away from you)
• The carbon chain runs vertically, with the most oxidized carbon typically at the top

A common mistake is rotating a Fischer projection 90° in the plane. This swaps the configuration at every center. You can rotate 180° (configuration preserved) but never 90°.

Newman projections show the conformation of a molecule as viewed along a specific C–C bond. The front carbon is a dot, the back carbon is a circle. These are most useful for analyzing steric strain and comparing staggered vs. eclipsed conformations, which helps you understand why certain diastereomers (like gauche vs. anti) differ in stability.